Arc length, sector area and shaded regions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Why mathematicians chose radians
- Degrees and radians
Read the transcript of the teaching part
Last time
Before we start: last time, in Tangents to a circle and a line and a circle, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Why mathematicians chose radians
Degrees come from the Babylonians, who liked the number three hundred and sixty. Radians come from the circle itself. One radian is the angle where the arc is as long as the radius. That makes the formulas for arcs and sectors beautifully short.
Degrees and radians
A half turn is one hundred and eighty degrees, which is pi radians. To change degrees to radians, multiply by pi over one hundred and eighty. Sixty degrees is pi over three. Thirty is pi over six. Ninety is pi over two. Keep pi in exact answers. Set your calculator to radians when a question gives pi.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Perimeter and area of a region · Sector and triangle areas.
The whole chapter: Circular Measure.
Chapter 1.4: Circular measure
- Arc length, sector area and shaded regions 6 min
- Circles and chords, sectors in r and theta, and tangents with sectors 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.